Theorem 1.6 ([1]}) 
Let \(X \rightarrow S\)  be a dominant morphism of integral varieties over a field \(K\) .
Assume that the set of \(s \in S(K)\)  for which the fibre \(X_s\)  is integral and satisfies the Hilbert property over \(K\) 
is not thin. Then \(X\)  satisfies the Hilbert property over \(K\) .

